Supreme Court nominee Brett Kavanaugh said a woman's allegation that he sexually assaulted her while both were in high school is "completely false" and that he's willing to talk to the Senate Judiciary Committee in any forum to "defend my integrity."

"This is a completely false allegation. I have never done anything like what the accuser describes - to her or to anyone," Kavanaugh said in a statement issued Monday by the White House. "Because this never happened, I had no idea who was making this accusation until she identified herself yesterday."

The woman who made the accusation, Christine Blasey Ford, also said she's willing to testify to Congress after prospects for a swift confirmation were put in doubt amid calls from key GOP senators for an investigation.

"She's willing to do whatever it takes to get her story forth," her attorney, Debra Katz, told NBC's "Today Show." Katz told CNN in a separate interview that Ford hasn't been contacted yet by the committee.

The White House reiterated its support for Kavanaugh, with spokeswoman Kerri Kupec saying in an email Monday that it stands by the nominee's denial.

GOP senators Bob Corker and Jeff Flake joined Democrats late Sunday in seeking to delay a crucial committee vote set for Thursday so lawmakers can further examine the allegations after the Washington Post published a detailed account from the accuser. Days earlier Kavanaugh had seemed on track for quick approval.

President Donald Trump won't withdraw the nomination and the administration is gearing up for a counteroffensive, a White House official said. The Trump team plans to try to discredit the charges for surfacing late in the confirmation process and to question the credibility of the accuser because she didn't tell anybody about the incident at the time, the official said.

The official said the White House wants to avoid a public hearing on the allegations -- a risky drama that could build sympathy for the accuser -- but is willing to accept a confidential inquiry. White House adviser Kellyanne Conway told reporters Monday that the accuser's allegations should be heard by the Senate.

"She should not be insulted, she should not be ignored, she should testify under oath and she should do it on Capitol Hill," Conway said. "But that's up to the Senate Judiciary Committee, they should decide the forum. And Judge Kavanaugh should also testify to these 36-year-old allegations."

One Judiciary Committee Republican, Flake of Arizona, told The Washington Post that Ford, "must be heard" before the panel's vote on the nomination, currently scheduled for Thursday.

"I've made it clear that I'm not comfortable moving ahead with the vote on Thursday if we have not heard her side of the story or explored this further," said Flake, who has the power to stall consideration if all Democrats on the panel join him since Republicans only hold an 11-10 majority on the committee. Flake's office didn't respond to requests for comment.

Corker of Tennessee, who isn't a member of the panel but whose vote is critical to confirmation, also doesn't want the committee to vote on Kavanaugh's confirmation until Ford's allegations can be heard, said his spokeswoman, Micah Johnson. The senator wants the allegations to be heard promptly, she said.

The Post identified Ford, a 51-year-old research psychologist and professor at Palo Alto University in California, as the woman whose accusation surfaced last week and raised the first serious doubts about Kavanaugh's confirmation. The newspaper quoted Ford's detailed description of the incident, and said it also viewed notes from a 2013 therapy session in which she had called it a "rape attempt."

Senate Judiciary Chairman Chuck Grassley is working to set up bipartisan staff conversations with Kavanaugh and Ford before Thursday's committee vote on the nomination, Grassley spokesman Taylor Foy said in an email Sunday evening.

Sen. Lisa Murkowski, a Republican from Alaska who is seen as crucial to Kavanaugh's prospects, told CNN that she's open to a delay in the committee vote. "If there are more questions that need to be asked and answered, then I think it would be appropriate for that time," she told the network.

Sen. Susan Collins of Maine, also seen as a pivotal GOP vote for the nomination, told the New York Times that she viewed the allegations as serious and Ford needs to be personally interviewed to gain more information. She said the delay in releasing the information wasn't fair to the accuser or Kavanaugh.

"If they believed Professor Ford, why didn't they surface this information earlier so that he could be questioned about it?" Collins said. "And if they didn't believe her and chose to withhold the information, why did they decide at the 11th hour to release it? It is really not fair to either of them the way it is was handled."

Sen. Dianne Feinstein, the top Judiciary Committee Democrat, said a staff call on the matter wasn't adequate.

"I agree with Senator Flake that we should delay this week's vote," Feinstein said in a statement. "There's a lot of information we don't know and the FBI should have the time it needs to investigate this new material."

The allegation puts heavy pressure on moderate senators who must decide whether to vote for Kavanaugh at the risk of angering the "Me Too" movement. That growing backlash against men facing claims of sexually abusing women has already forced the resignations of top executives and some lawmakers. Republican Senators Susan Collins of Maine and Lisa Murkowski of Alaska haven't said whether they'll vote to confirm Kavanaugh, nor have a handful of Democrats from states that backed Trump in 2016.

It's also a significant challenge for Republicans who are struggling to win suburban women's votes in the Nov. 6 election that will decide control of the U.S. House and Senate.

Don Stewart, a spokesman for Senate Majority Leader Mitch McConnell, said the Republican senator doesn't have any immediate comment about the matter.

Foy, Grassley's spokesman, said in an earlier statement that it was "disturbing that these uncorroborated allegations" had surfaced shortly before Thursday's planned committee vote. The statement didn't say whether there would be any schedule change, and Foy didn't immediately respond to a query on the issue. Republicans are aiming for full Senate confirmation of Kavanaugh before the Supreme Court term begins Oct. 1.

Republican Sen. Lindsey Graham of South Carolina, also a Judiciary Committee member, said that if Ford wants to provide information to the committee, "I would gladly listen to what she has to say." But he said that should be done immediately, "so the process can continue as scheduled."

The White House on Friday released a statement from Kavanaugh in which the nominee said, "I categorically and unequivocally deny this allegation. I did not do this back in high school or at any time."

The controversy comes 27 years after the bruising confirmation of Supreme Court Justice Clarence Thomas, who was accused of sexually harassing attorney Anita Hill at two federal jobs, including when he chaired the U.S. Equal Employment Opportunity Commission that handles harassment and discrimination issues. Thomas was confirmed on a 52-48 vote.

Sunday's development threatens what would be a major win for Trump's White House and McConnell, as they seek to give a strong rightward tilt to the federal judiciary. White House Counsel Donald McGahn, a leading architect of the strategy, has been due to leave the White House once Kavanaugh is confirmed, after it was disclosed that he was cooperating with Special Counsel Robert Mueller's probe into Russian election meddling.

Republicans control the Senate 51-49, meaning they need no Democratic support to confirm Kavanaugh, but the outcome likely depends on pro-choice Senators Collins and Murkowski, neither of whom responded to requests for comment Sunday. Kavanaugh could provide the fifth vote to overturn the Roe v. Wade abortion-rights decision. He called Roe an "important precedent" during his Senate Judiciary confirmation hearing but refused to say whether the ruling was correct.

Kavanaugh's potential impact on the abortion debate is a risk to the GOP's already lackluster standing with women, and the sexual assault allegation could make things worse. Female voters preferred Democratic candidates over Republican ones by 54 percent to 33 percent, while 62 percent of women disapproved of Trump's job performance, according to an NPR/PBS NewsHour/Marist poll in July.

The Post quoted Ford as saying Kavanaugh and a friend were "stumbling drunk" when they took her into a bedroom during a party in a house in the Maryland suburbs of Washington. Kavanaugh pinned her to the bed and groped her through her clothes, grinding his body against hers and trying to pull off her clothes, the Post quoted Ford as saying. She said that when she tried to scream, he put his hand over her mouth. She said she believed the attack occurred in 1982.

"I thought he might inadvertently kill me," the Post quoted Ford as saying. She said Kavanaugh's friend, Mark Judge, jumped on top of them, sending them tumbling, and she was able to escape, the newspaper reported. She said she went home and didn't tell anyone until she and her husband were in couples therapy in 2012.

The Post said it viewed notes from that session and an individual therapy session the following year. The paper said the 2013 notes showed that Ford described a "rape attempt" in her late teens. Her husband, Russell Ford, told the newspaper that when she described the incident in the 2012 session, she used Kavanaugh's last name and said she was concerned he might eventually be nominated to the Supreme Court. He has been a federal appeals court judge since 2006.